(−2k3−7k2+5k)+(6k2+3k)

Jasonbradley

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Jun 17, 2024

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Simplifying Algebraic Expressions: (−2k3−7k2+5k)+(6k2+3k)

This article will walk you through the steps of simplifying the algebraic expression: (−2k3−7k2+5k)+(6k2+3k).

Understanding the Problem

We are given two expressions enclosed in parentheses and asked to add them together. To do this, we'll utilize the associative property of addition which states that the order in which we add multiple terms doesn't change the sum.

Step-by-Step Solution

1. Remove the parentheses: Since we are adding the expressions, the parentheses don't affect the order of operations.

   (−2k3−7k2+5k)+(6k2+3k) becomes −2k3−7k2+5k+6k2+3k

2. Combine like terms: Identify terms with the same variable and exponent.

   • k3 terms: −2k3 (This is the only k3 term)
   • k2 terms: −7k2 + 6k2
   • k terms: 5k + 3k

3. Simplify: Perform the addition or subtraction of the coefficients for each group of like terms.

   • k3 terms: −2k3
   • k2 terms: −7k2 + 6k2 = −k2
   • k terms: 5k + 3k = 8k

4. Write the simplified expression: Combine the simplified terms.

   −2k3 − k2 + 8k

Conclusion

The simplified form of the expression (−2k3−7k2+5k)+(6k2+3k) is −2k3 − k2 + 8k. Remember to always combine like terms and pay attention to the signs of the coefficients.